Inclusion Theorems of Certain Integral Transform Related to Normalized Hypergeometric Functions and Generalized Bessel Functions

This study explores the geometric properties of normalized Gaussian hypergeometric functions in a certain subclass of analytic functions. This work investigates the inclusion properties of integral operators associated with generalized Bessel functions of the first kind. By finding the conditions on the parameters of the Gaussian hypergeometric function, we identify criteria for the normalized Gaussian hypergeometric function to be in a certain subclass of analytic functions. Using Taylor coefficients, we obtained sufficient conditions for the integral operators associated with generalized Bessel functions of the first kind to belong to different subclasses of univalent functions. The results obtained are analyzed and compared with the existing literature, providing new insights into the subclasses.